(4x+y)(7x-6y)=

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Solution for (4x+y)(7x-6y)= equation: 


Simplifying
(4x + y)(7x + -6y) = 0

Multiply (4x + y) * (7x + -6y)
(4x * (7x + -6y) + y(7x + -6y)) = 0
((7x * 4x + -6y * 4x) + y(7x + -6y)) = 0

Reorder the terms:
((-24xy + 28x2) + y(7x + -6y)) = 0
((-24xy + 28x2) + y(7x + -6y)) = 0
(-24xy + 28x2 + (7x * y + -6y * y)) = 0
(-24xy + 28x2 + (7xy + -6y2)) = 0

Reorder the terms:
(-24xy + 7xy + 28x2 + -6y2) = 0

Combine like terms: -24xy + 7xy = -17xy
(-17xy + 28x2 + -6y2) = 0

Solving
-17xy + 28x2 + -6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -6y)(4x + y) = 0


Subproblem 1
Set the factor '(7x + -6y)' equal to zero and attempt to solve:

Simplifying
7x + -6y = 0

Solving
7x + -6y = 0

Move all terms containing x to the left, all other terms to the right.

Add '6y' to each side of the equation.
7x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
7x + 0 = 0 + 6y
7x = 0 + 6y
Remove the zero:
7x = 6y

Divide each side by '7'.
x = 0.8571428571y

Simplifying
x = 0.8571428571y

Subproblem 2
Set the factor '(4x + y)' equal to zero and attempt to solve:

Simplifying
4x + y = 0

Solving
4x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
4x + 0 = 0 + -1y
4x = 0 + -1y
Remove the zero:
4x = -1y

Divide each side by '4'.
x = -0.25y

Simplifying
x = -0.25y
Solution
x = {0.8571428571y, -0.25y}

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